DOVER-FOXCROFT, Maine — Janet Flaherty got an alarming call last October from the agency tasked with coordinating in-home care for her 82-year-old mother. It could no longer send her mom’s home caretaker. It knew of no other aides who could care for her mother, either.

Flaherty’s mother, Caroline, has for two years qualified for in-home care paid for by the state’s Medicaid program. But the agency could not find someone to hire amid a severe shortage of workers that has crippled facilities for seniors across the state.

With private help now bid up to $50 an hour, Janet and her two sisters have been forced to do what millions of families in a rapidly aging America have done: take up second, unpaid jobs caring full time for their mother.